Solution: The intersection of straight line kx+(k+ 1)y= 1(k is a positive integer) and two coordinate axes is:

( 1/k，0)[0， 1/(k+ 1)]

The area of a closed figure.

sk = 1/2 * 1/k * 1/(k+ 1)= 1/[2k(k+ 1)]

So S 1+S2+S3+…+S2000.

= 1/2[ 1/( 1*2)+ 1/(2*3)+ 1/(3*4)+ 1/(4*5)+……+ 1/( 1999*2000)]

= 1/2( 1/ 1- 1/2+ 1/2- 1/3+ 1/3- 1/4+ 1/4- 1/5+……+ 1/ 1999- 1/2000)

= 1/2( 1- 1/2000)

= 1/2* 1999/2000

= 1999/4000